Ruin probabilities in the presence of heavy-tails and interest rates

Ulrich Stadtmüller, Claudia Klüppelberg

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88 Scopus citations


We study the infinite time ruin probability for the classical Cramér-Lundberg model, where the company also receives interest on its reserve. We consider the large claims case, where the claim size distribution F has a regularly varying tail. Hence our results apply for instance to Pareto, loggamma, certain Benktander and stable claim size distributions. We prove that for a positive force of interest δ the ruin probability ψδ(u) ∼ κδ(1 - F(u)) as the initial risk reserve u→∞. This is quantitatively different from the non-interest model, where ψ(u) ∼ κ (1 – F(y)) dy.

Original languageEnglish
Pages (from-to)49-58
Number of pages10
JournalScandinavian Actuarial Journal
Issue number1
StatePublished - 1 Jan 1998
Externally publishedYes


  • Abel-Tauber theorems
  • Heavy tails
  • Interest rate model
  • Modified Laplace transforms
  • Regular variation
  • Ruin probability


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